What A Perfect Bracket Looks Like, Part 2

As promised in a previous article, I will try to apply a predictive tool that will better guide us in using the Aggregation Model (AM). If this predictive tool is accurate in forecasting which Aggregate Value (AV) to use, then we should be able to approximate which Elite 8 Seed Pairs (E8SP) to use so that they match the expected Aggregate Value. The predictive tool being used to forecast the AM is the Seed Curve. If you are unfamiliar with the Seed Curve, see this article; and if you are unfamiliar with the AM, AVs or E8SPs, then re-read Part 1 of this article linked in the opening sentence.

First, let's take a collective look at things, and then we'll look at the group perspective. Below is the AM from 2003-2015 displaying each of those year's AVs.

Collective Analysis

1. The steepness or flatness of a given curve should tell us about the relative quality of the tournament teams. Steeper curves suggest top seeds are relatively stronger than bottom seeds (top-seed dominance) whereas flatter curves suggest the top seeds are relatively weaker than bottom seeds (parity). The steeper curves appear to be 2007, 2008, and 2015. These three years also happen to be among the curves with lower AVs. The flatter curves appear to be 2004, 2010, and 2011. These three years also happen to be among the curves with higher AVs.
2. The peaks and troughs of a given curve should tell us about the seed placement of teams. If teams are seeded in order of efficiency rankings, then the SC would decline at a steady rate (like the QC does). If teams are seeded out of order from their efficiency rankings, then it could increase the chances of upsets. If teams that should be 9s or 10s get seeded as 11s or 12s, then 6s and 5s (respectively) now have a tougher match-up than they should.

Comparative Analysis

In the previous article, the AVs for the past 13 tournaments were grouped together in 5 groups according to their similarities. In this part of the analysis, these 5 groupings will be used to determine if there is a correlation between the SCs and the AVs. We'll start with the two extreme groups: 1) the Sanity Group of 2007/2009 which produced the lowest AVs in those 13 years and 2) the Insanity Group of 2011/2014 which produced the highest AVs in those 13 years.

First up, the Sanity Group. There are some striking similarities between these two SCs. The SC starts off around .9500 level, steadily declines thru the 5-seed, spikes up at the 6 and 8-seeds, and a down-flat-sharply down pattern from 10-13. The 2007 year showed unusual strength at the 8- and 9-seeds, but none were able to pull upsets as all four 1-seeds made the E8 in both years. Both SCs altogether are rather steep, starting high and ending low, which should predict a top-seed dominant tournament. Let's look at the Insanity Group.

There are some striking similarities between these two SCs as well. Both curves start with cupping action from 1- to 4-seeds, declines into 5-seeds, flattening from 6 to 9, decline to 10, rise to 11, and a steep decline at 13. If we look at the chart from the perspective of generic E8SPs, then it really gets interesting. In 2011, 4s are strong, 8s and 9s do not see sharp declines, the 12s are rather high, and the 13s are an entire 0.0500 higher than the 13s in 2014. No wonder 1-seeds had so much trouble in both these years!, producing an just 3 out of a possible 8 E8SPs. On the other side, 2s are a sharp drop-off from the 1s with 3s near the same level, 6s and 7s are relatively strong, and 11s are above the .8000 level. Both years produced two 2-seeds and an 11-seed, and the 11 should not come as a surprise with such little resistance in route to the E8. Let's try our luck with a moderate pair.

Before pointing out the features of the SC, not only did both of these years produce the same AV, but they did so by producing the exact same E8SPs (obviously if your E8SPs are exactly the same, then the sum of them, which produces the AV, will be the exact same). These two SCs present similar patterns, but the patterns do not present on the same intervals like they do in the previous two groups. For example, the SCs start with outward bowing: 2012 goes from 1-3 whereas 2015 goes from 1-4. Then, they proceed with some flattening: 2012 from 3-5 and 2015 from 4-7. Then, both roughly show some descending oscillations: 2012 oscillates from 5-8, declines, then oscillates again from 11-13 whereas 2015 oscillates from 7-11 and then just declines the rest of the way. An outward bowing curve indicates that the drop-off from the previous seed is not as great as the drop-off to the next seed. The one noticeable difference among these two SCs is the difference in steepness. The 2012 SC starts just under .9500 and declines to just below .7500 (a drop of .2000 from 1-13). The 2015 SC starts around .9600 and declines to .6700 (almost a drop of .3000 thru the same range). With such a noticeable difference in curve-steepness, it seems strange that both SCs would produce identical E8SPs. Then again, it may be a combination of curve steepness and pattern timing that caused the identical results.

I feel like the concepts that I have described in the three analyses above are indicative of a relationship between SCs and the AVs they produce. Typically, I would exhaust this analysis by doing all five groups, but the patterns within each group are rather identifiable and my analysis would be akin to beating a dead horse. Instead, I will present the remaining two groups, and the followers of PPB can debate it in the comment section.

My next article should be on Mon, Feb 1 before the start of the new week of games. As promised, it will be the February Edition of Quality Curve Analysis (which will comprise all games thru Jan 31).